Galaxy emission line classification using 3D line ratio diagrams

Download PDF
6 downloads 45491 Views 14MB Size Report
Comment
Jun 19, 2014 - cleanly separate H II region-like objects from the different classes of AGNs. ..... Accessing the interactive model requires Adobe Acrobat.
Draft version June 23, 2014 Preprint typeset using LATEX style emulateapj v. 5/2/11

GALAXY EMISSION LINE CLASSIFICATION USING 3D LINE RATIO DIAGRAMS ´ de ´ric P.A. Vogt1,2 , Michael A. Dopita1,3,4 , Lisa J. Kewley1,4 , Ralph S. Sutherland1 , Fre ¨ chter5 , Hassan M. Basurah 3 , Alaa Ali3,6 & Morsi A. Amer3,6 Julia Scharwa

arXiv:1406.5186v1 [astro-ph.GA] 19 Jun 2014

Draft version June 23, 2014

ABSTRACT Two-dimensional (2D) line ratio diagnostic diagrams have become a key tool in understanding the excitation mechanisms of galaxies. The curves used to separate the different regions - H II-like or else excited by an active galactic nucleus (AGN) - have been refined over time but the core technique has not evolved significantly. However, the classification of galaxies based on their emission line ratios really is a multi-dimensional problem. Here we exploit recent software developments to explore the potential of three-dimensional (3D) line ratio diagnostic diagrams. We introduce a specific set of 3D diagrams, the ZQE diagrams, which separate the oxygen abundance and the ionisation parameter of H II region-like spectra, and which also enable us to probe the excitation mechanism of the gas. By examining these new 3D spaces interactively, we define a new set of 2D diagnostics, the ZE diagnostics, which can provide the metallicity of objects excited by hot young stars, and which cleanly separate H II region-like objects from the different classes of AGNs. We show that these ZE diagnostics are consistent with the key log[N II]/Hα vs. log[O III]/Hβ diagnostic currently used by the community. They also have the advantage of attaching a probability that a given object belongs to one class or to the other. Finally, we discuss briefly why ZQE diagrams can provide a new way to differentiate and study the different classes of AGNs in anticipation of a dedicated follow-up study. Subject headings: galaxies: abundances, galaxies: starburst, galaxies: Seyfert, galaxies: general, ISM: lines and bands, H II regions 1. INTRODUCTION

The use of specific line ratios to distinguish line emission regions depending on their gas excitation mechanism was pioneered by Baldwin et al. (1981) and extended by Veilleux & Osterbrock (1987). The line ratios most frequently used, specifically designed to be insensitive to reddening, are: 1. log[N II]/Hα vs. log[O III]/Hβ, 2. log[S II]/Hα vs. log[O III]/Hβ and 3. log[O I]/Hα vs. log[O III]/Hβ. Theoretical progress has since allowed the placement of different diagnostic lines separating the different excitation mechanisms in these diagrams: regions photoionised by hot stars giving H ii-like spectra, regions excited by an Active Galactic Nucleus (AGN), either Seyferts, or the low ionization nuclear emission-line regions (LINERs). Currently, the maximum starburst lines from Kewley et al. (2001b,a), the empirical starburst line from Kauffmann et al. (2003b), and the LINER-Seyfert lines from [email protected] 1 Research School of Astronomy and Astrophysics, Australian National University, Canberra, ACT 2611, Australia. 2 Department of Physics and Astronomy, Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218, USA. 3 Astronomy Department, King Abdulaziz University, P.O. Box 80203, Jeddah, Saudi Arabia. 4 Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA. 5 Observatoire de Paris, LERMA (CNRS: UMR8112), 61 Av. de l’Observatoire, 75014 Paris, France. 6 Astronomy Department, Faculty of Science, Cairo University, Egypt.

Kewley et al. (2006) are commonly used. Other, similar diagnostics include Heckman (1980); Osterbrock & Pogge (1985); Veilleux & Osterbrock (1987); Tresse et al. (1996); Ho et al. (1997); Dopita et al. (2000); Stasi´ nska et al. (2006). The maximum starburst lines as defined by Kewley et al. (2001a) are based on theoretical modelling of starburst galaxies. Specifically, the wrap-round of theoretical model grids inside these optical line ratio diagnostic diagrams justifies the definition of a theoretical upper bound of emission line ratios from gas photoionised by hot young stars. Kauffmann et al. (2003b) used the large number statistics of the Sloan Digital Sky Survey (SDSS, York et al. 2000) to set an observational lower bound to the maximum starburst line in the log[N II]/Hα vs. log[O III]/Hβ diagram. The region between these two starburst lines is known as the “composite” region. Recently, several objects in the composite region have been recognised as being (at least in part) excited by shocks (Farage et al. 2010; Rich et al. 2011, 2013), although these do not rule out a mixed excitation mechanism (starburst+AGN) for other composite objects (e.g. Scharw¨achter et al. 2011; Davies et al. 2014; Dopita et al. 2014b). Kewley et al. (2006) also exploited the large number statistics from SDSS to define the separation lines between the LINER and the Seyfert branches on the AGN side of the log[S II]/Hα vs. log[O III]/Hβ and log[O I]/Hα vs. log[O III]/Hβ diagrams. The classical optical line ratio diagnostic diagrams have proved to be useful and resilient, ever since their introduction. Recently, their usage has been extended as new IR surveys of galaxies measure the key line ratios for galaxies at intermediate and high redshifts. The key instruments are MOSFIRE on Keck (McLean et al.

2

Vogt et al.

2010), FMOS on Subaru (Kimura et al. 2010), MMIRS on Magellan (McLeod et al. 2004), FLAMINGOS II on Gemini (Eikenberry et al. 2008) and LUCI at the Large Binocular Telescope (Buschkamp et al. 2012). The sensitivity of the optical line ratio diagnostics to metallicity and other factors which could influence the diagnostics at high-redshift was investigated by Kewley et al. (2013a), and this insight was applied to actual samples of highredshift galaxies by Kewley et al. (2013b). A further stimulus to the use of optical line ratio diagnostic diagrams has been the advent of integral field spectrographs (IFS). These instruments provide spectral information for individual spectral pixels (commonly referred to as spaxels). With this approach, it is possible to reveal the presence of metallicity gradients across the entire spatial extent of galaxies (Rich et al. 2012), explore the trends in the local excitation pressure (Dopita et al. 2014a), or study the AGN zone of influence (Scharw¨ achter et al. 2011). These analyses, in turn, rely on an accurate classification scheme. In reality, the full set of line ratios forms a multidimensional space, the topology of which needs to be understood before a final classification can be set. Progress towards this goal can be made by looking at alternative line ratio diagrams. For the case of H II regions, Dopita et al. (2013) made a comprehensive study of the utility of alternative diagnostic diagrams, discussing previously used ones, as well as introducing some new ones. Few of these diagrams separate the AGN branch from the stellar excited objects as well as the traditional log[N II]/Hα vs. log[O III]/Hβ diagram. Notable exceptions are provided by the log[N II]/Hα vs. log[O III]/[O II] diagram and the log[N II]/[O II] vs. log[O III]/Hβ diagram. In this paper, we revisit the concept of optical line ratio diagram itself, and introduce new 3D line ratio diagrams. These diagrams, combining three different and complimentary line ratios, are a first step towards a better understanding of the distribution of galaxies in their multi-dimensional line ratio space. This article is organized as follows. We first describe the observational datasets that we employ in our analysis in Section 2, and the theoretical models we use in Section 3. We introduce the new 3D line ratio diagrams derived from these datasets in Section 4. In Section 5, we use specific 3D line ratio diagrams to generate a new and consistent set of line ratio diagnostics to separate H II-like galaxies from the AGN-like objects. In Section 6, we compare these new diagnostics with the standard optical line ratio diagnostic diagrams, and discuss their compatibility with intermediate and high redshifts spectroscopic observations. Finally, we highlight the potential of these new 3D line ratio diagrams to investigate the different AGN families in Section 7, and summarise our conclusions in Section 8. 2. OBSERVATIONAL DATASETS

2.1. SDSS galaxies We construct our sample of emission line galaxies from the Sloan Digital Sky Survey (SDSS) data release (DR) 8 (Aihara et al. 2011b,a; Eisenstein et al. 2011). Specifically, we exploit the “galSpec” Value Added Catalogue from the Max Planck Institute for Astronomy and Johns Hopkins University (MPA-JHU) group. The data is in

fact identical to that associated with the SDSS DR7 (Abazajian et al. 2009), but was first made accessible via the general SDSS data release in DR8. This dataset has been freely accessible since the SDSS DR4 (AdelmanMcCarthy et al. 2006), and the associated fitting procedure for the stellar continuum and emission lines are described in detail in Kauffmann et al. (2003a); Brinchmann et al. (2004); Tremonti et al. (2004). Each spectrum is corrected for the foreground Galactic extinction using the O’Donnell (1994) extinction curve. The stellar continuum is fitted with a linear combination of ten single-age stellar population models based on a new version of the GALEXEV code of Bruzual & Charlot (2003, 2011) plus an additional parameter accounting for internal dust attenuation (Charlot & Fall 2000). The different emission lines are fitted with single Gaussians. Balmer lines share a unique rest-frame velocity and velocity dispersion (accounting for the instrumental resolution), and so do the forbidden lines. From the 1843200 objects provided in DR8, we extract a sub-sample of high-quality spectra with reliable galSpec fit parameters, following the methodology of Kewley et al. (2006). Our detailed selection criteria (including the explicit SDSS keywords expressions) are: 1. an existing galSpec fit (i.e. [PLATEID;FIBERID;MJD] 6= -1), 2. the galSpec fit is flagged as “reliable” by the MPAJHU group (i.e. RELIABLE = 1), 3. a reliable redshift measurement (i.e. Z WARNING = 0), 4. a redshift between 0.04 and 0.1 (i.e. 0.04 < Z < 0.1), 5. a signal-to-noise ≥ 3 in the following strong lines: [O II]λ3726, [O II]λ3729, Hβ, [O III]λ5007, Hα, [N ii]λ6584, [S II]λ6717 and [S II]λ6731, 6. a signal-to-noise ≥ 3 for the continuum measurement around Hβ, and 7. Hα/Hβcorr ≥ 2.86. The redshift selection is identical to Kewley et al. (2006): the lower limit ensures that at least 20% of the galaxy is covered by the 3 arcseconds fiber of the SDSS spectrograph, so that the spectra is representative of the global properties of the galaxy (Kewley et al. 2005). The higher redshift bound is designed to ensure the completeness of the LINER class, comparatively dimmer than Seyferts. We calculated the S/N of each emission lines from the line flux and its associated error scaled by the amount suggested by Juneau et al. (2014) (see Table 1). These correction factors have been obtained by comparing the different duplicate observations in the dataset, and are lower than the values recommended by the MPAJHU group for their DR4 Value Added Catalogue. Following the recommendation of Groves et al. (2012), we also add 0.35˚ A to the equivalent width of Hβ (with Hβcorr the corrected line flux), which was found to be underestimated because of an error in the 2008 version of the GALEXEV code (Bruzual & Charlot 2011). Hence, we require the continuum level around Hβ to have S/N≥ 3 to

Three-dimensional Line Ratio Diagrams ensure a reliable correction. The median correction for our sample is ∼6% of the original Hβ flux. TABLE 1 Corrections applied to the errors of emission line fluxes. Line

Correction

[O II]λ3726

1.33

[O II]λ3729

1.33

Hβ

1.29

[O III]λ5007

1.33

[O I]λ6300

1.02

Hα

2.06

[N II]λ6584

1.44

[S II]λ6717

1.36

[S II]λ6731

1.36

3

of an AGN can result in an higher intrinsic Balmer ratio (i.e. Rαβ ∼ = 3.1, e.g. Osterbrock 1989; Kewley et al. 2006). However, it is unclear what intrinsic ratio should be applied for “composite” objects possibly containing a mix of star-formation and AGN. Hence, we use an intrinsic Balmer ratio of 2.86 to ensure a uniform sample without artificial separation. For consistency, we will indicate visually in all line ratio diagrams throughout this article the spatial displacement ζ associated with a intrinsic Balmer decrement Rαβ =3.1 instead of 2.86. Analytically, for an observed line ratio Fλ1 /Fλ2 , we can write using Eq. 2 : Fλ1 ,0 Fλ1 = · Fλ2 ,0 Fλ2



2.86 Rαβ

λ1  ττλ2 −τ −τ Hα

Hβ

τλ =

Eλ−V + RVA , EB−V

so that

We have removed duplicate observations in the sample using our own Python routine. For every galaxy, we look for all other objects located within 3 arcseconds (with no restriction on the redshift), and remove them all from our sample except for the one with the largest S/N(Hα). Our final sample is comprised of 105070 galaxies. 2.1.1. Extragalactic reddening correction We correct the emission line fluxes for extragalactic reddening based on the Balmer decrement Rαβ , using the extinction law from Fischera & Dopita (2005) for RA V =4.5 (and AV =1). This extinction law is very close to that of Calzetti et al. (2000) for starburst galaxies, and Wijesinghe et al. (2011) have shown that it provides very good agreement between different SFR indicators ([O II],Hα, near-UV, far-UV) for the GAMA galaxies (Driver et al. 2009). Specifically, we follow the procedure described in detail in Appendix A of Vogt et al. (2013), with: Eλ−V = −4.61777 + 1.41612 · λ−1 + 1.52077 · λ−2 EB−V −0.63269 · λ−3 + 0.07386 · λ−4 (1) where λ is in µm, and the actual reddening correction is given by :

Fλ,0 = Fλ ·

FHα /FHβ Rαβ

Eλ−V A +RV EB−V Hα−V − EHβ−V EB−V EB−V

·

FHα /FHβ 2.86

λ1  ττλ2 −τ −τ Hα

Hβ

,

(3) where

Note: although S/N([O I]λ6300) is not used in our sample selection, the associated error scaling correction is included here for completeness.





− E

(2)

with Fλ,0 the intrinsic emission line flux, Fλ the measured emission line flux, λ the rest-frame emission line wavelength, and in our case, RVA = 4.5. We adopt an intrinsic Balmer ratio Rαβ = 2.86 corresponding to Case B recombination for every object in our sample, irrespective of their classification. This value is appropriate for star-forming galaxies, but the presence

 ζ(λ1 , λ2 ) =

2.86 Rαβ

(4)

λ1  ττλ2 −τ −τ Hα

Hβ

.

(5)

As we will discuss in the next Sections, ζ is small enough so that the choice of Rαβ is not critical to our analysis. Especially, as we will focus on the separation between AGN-dominated and star-forming galaxies, the objects located close-to or on the classification diagnostic lines (i.e. with very little AGN influence) can be expected to have Rαβ ∼ = 2.86. As mentioned above, we have removed ∼200 galaxies with measured Hα/Hβ < 2.86 from our sample, under the assumptions that these low ratios are indicative of observational and/or fitting issues. After correcting the emission line fluxes for extragalactic reddening, our sample contains 88933 (84.6%) galaxies classified as star-forming, 11447 (10.9%) classified as composites and 4690 (4.5%) classified as AGN-dominated, based solely on their position in the log[N II]/Hα vs. log[O III]/Hβ diagram. 2.2. H II region spectra Since the SDSS spectra represent nuclear spectra of whole galaxies, it is important for classification purposes that we also have a set of well-observed isolated H II regions covering a wide range of chemical abundances. For this purpose we adopt the excellent homogeneous dataset from van Zee et al. (1998). This dataset is somewhat deficient in the most metal rich objects, so we have supplemented the van Zee et al. (1998) H II regions with our own data on the H II regions in the Seyfert galaxy NGC 5427. These bright H II regions are unaffected by the weak Seyfert 2 nucleus, and their abundances range up to three times solar. We refer the reader to Dopita et al. (2014b) for more details on the observations, data reduction and emission line flux measurements for these H II regions. 3. THE THEORETICAL H II REGION MODELS

Throughout this article, we rely on the grids of line intensities for H II regions derived from the modelling code MAPPINGS IV by Dopita et al. (2013). These

4

Vogt et al.

grids cover a wide range of abundances (5 − 0.05 Z ) and ionisation parameters (6.5 . log q . 8.5). MAPPINGS IV is the latest evolution of the MAPPINGS code (Dopita et al. 1982; Binette et al. 1982, 1985; Sutherland & Dopita 1993; Groves et al. 2004; Allen et al. 2008), that (among other updates) can now account for the possible non-Maxwellian energy distribution of electrons in astrophysical plasmas. The idea that the energy distribution of electrons in planetary nebulae and H II regions may depart from a standard Maxwell-Boltzmann distribution to resemble a κdistribution, characterised by a high-energy tail, was recently suggested by Nicholls et al. (2012). The consequences of a κ-distribution of electron energies on temperature and abundance measurements in H II regions have been discussed in detail by Nicholls et al. (2013) and in respect of the effect on strong line intensities by Dopita et al. (2013). For these, the effect of a κ-distribution is only minor, and does not significantly affect our analysis. Throughout this paper, we have adopted κ = 20. 4. CREATING 3D LINE RATIO DIAGRAMS

There is a priori no reason to restrict line ratio diagrams to 2 dimensions, other than the evident practicality of visualisation. Here, we exploit recent software developments to explore the potential of 3D line ratio diagrams. The basic concept is as follows. As a starting point we use the 2D diagnostics from Dopita et al. (2013) which cleanly separate the ionisation parameter, q, and the oxygen abundance, 12 + log(O/H). We then couple them with an additional line ratio, chosen specifically to help differentiate H II-like objects from AGNs. This third ratio ought to be more sensitive to the hardness of the radiation field. In Table 2, we list the different line ratios used for each of the three categories; • Category I: abundance sensitive ratios, • Category II: q- sensitive ratios, and • Category III: radiation hardness-sensitive ratios. In practice, of course, the separation is not as clean as implied by this list, since each ratio is in some part sensitive to all three parameters we are trying to dissociate. Nonetheless the exercise remains useful as a means of teasing out these parameters. TABLE 2 Line ratios and associated keys. Category I Key Ratio

Category II Key Ratio

Category III Key Ratio

a:

log

[N ii] [O ii]

c:

log

[O iii] [O ii]

f:

log

[O iii] Hβ

b:

log

[N ii] [S ii]

d:

log

[O iii] [S ii]

g:

log

[N ii] Hα

e:

log

[O iii] [N ii]

h:

log

[S ii] Hα

i:

log

[O i] Hα

Note: throughout this paper and unless noted otherwise, when we refer to specific emission lines we mean [N ii]≡[N ii]λ6583, [S ii]≡[S ii]λ6717+λ6731, [O ii]≡[O ii]λ3727+λ3729, [O iii]≡[O iii]λ5007 and [O i]≡[O i]λ6300.

We restrict ourselves to ratios involving (usually) intense emission lines commonly observed in both H II regions and AGN-dominated objects. To each ratio we associate a “key”, defined in Table 2, to unambiguously identify them throughout this paper. One example of a 3D line ratio diagram (log[N II]/[O II] vs. log[O III]/[S II] vs. log[N II]/Hα) is shown in Figure 1. Figure 1 is interactive, and allows the reader to freely rotate, zoom in/out and/or fly through the 3D diagram.7 Figure 1 is also 3D printable using the STL file provided as supplementary material (see Appendix B for more details). We refer to these new 3D line ratio diagrams as ZQE diagrams, following the categorisation of the line ratios involved. To uniquely identify all possible ZQE diagrams, we attach the key of the three line ratios involved (in the order defining a right-handed orthogonal base), in the form of ZQE x1 x2 x3 , where x1 ,x2 and x3 corresponds to keys of line ratios in the Category I, II and III defined in Table 2. For example, the 3D line ratio diagram shown in Figure 1 is ZQE adg . In this new 3D diagram, the spatial structure of the cloud of points of SDSS galaxies resemble that of a nudibranch. H II-like objects are located on, or close to, the photoionization model grid and can be associated with the sea slug’s body. This sequence is clearly separated from the AGN sequence, which extends away from the H II region model grid (and which can be regarded as the “feelers” of the nudibranch). These AGN-dominated regions also display a clear substructure in the spatial density of galaxies, best revealed in the interactive version of Figure 1. From the line ratios listed in Table 2, it is possible to construct 2 × 3 × 4 = 24 different 3D spaces combining one ratio of each category, and we list them all in Table 3 with their ZQE denomination. 4.1. Exploiting ZQE diagrams One of the key advantages of ZQE diagrams is the ability to inspect them interactively (in a similar manner to the interactive counterpart of Figure 1). Following this approach, it is possible to identify new points of view of interest on the multi-dimensional space of galaxy line ratios. Working interactively with 3D line ratio diagrams may seem (at first) cumbersome. As we will argue here, it really is not the case anymore. We rely on the Python module Mayavi2 to create our interactive 3D diagrams (Ramachandran & Varoquaux 2011). We refer the reader to the full package documentation available online8 . Mayavi2 is a module dedicated to “3D scientific data visualization and plotting in Python”. It is in some ways reminiscent of the Matplotlib module dedicated to 2D plotting (Hunter 2007). We stress here that unlike dedicated computer-assisted design (CAD) softwares, using Mayavi2 does not require any specific knowledge a priori. The module syntax is relatively in7 Accessing the interactive model requires Adobe Acrobat Reader v9.0 or above, which is freely accessible. This figure, which follows a concept described by Barnes & Fluke (2008), was created using the Python module Mayavi2 (Ramachandran & Varoquaux 2011), and the commercial software PDF3D, similarly to the interactive counterpart of Figure 9 in Vogt & Shingles (2013). 8 http://docs.enthought.com/mayavi/mayavi/, accessed on October 29th, 2013.

Three-dimensional Line Ratio Diagrams

5

Fig. 1.— Example of a 3D line ratio diagram, labelled ZQE adg (a.k.a. log[N II]/[O II] vs. log[O III]/[S II] vs log[N II]/Hα), in the form of a cross-eyed stereo pair. The plane of MAPPINGS IV simulations of H ii regions is represented by the coloured spheres connected by the grey rods, where each sphere corresponds to one distinct simulation. The colour indicates the oxygen abundance in terms of 12 + log(O/H). Individual cubes correspond the van Zee et al. (1998) data points, and the small cones to the NCG 5472 measurements of individual H II regions, also coloured as a function of their metallicity. Detailed instructions to view this cross-eyed stereo pair can be found in Vogt & Wagner (2012). An interactive version of this Figure, that allows the reader to freely rotate and/or zoom in and out, can be accessed by using Adobe Acrobat Reader v9.0 or above. In the interactive model, the red, green and blue axes correspond to the log[N II]/[O II], log[O III]/[S II] and log[N II]/Hα directions, respectively.

tuitive, as illustrated by the basic examples available online9 . Similarly to other Python modules, Mayavi2 can be integrated seamlessly in any given Python script, and within a few lines, allows the creation of an interactive 3D model, for example a ZQE diagram. We note that in addition to a ”cursor-based” approach, the interactive diagrams generated with Mayavi2 can also be manipulated from a Python shell and scripts. Readers with practical questions regarding the implementations of interactive 3D diagrams with Python are welcome to contact us. At the time of publication of this article, the interactive 3D models generated by Mayavi2 cannot be directly integrated in documents in a Portable Document Format (PDF). While Mayavi2 can save 3D models in different dedicated file formats (e.g. .VRML, .OBJ, .IV), an additional step is required to transform these in the U3D format, compatible for inclusion in PDF documents. For this article, we relied on the commercial software PDF3DReportGen to transform the VRML file generated by Mayavi into a .U3D file, and included it in this article with pdftex and the media9 package in LATEX.

9

http://docs.enthought.com/mayavi/mayavi/auto/examples. html

5. FROM 3D ZQE DIAGRAMS TO NEW 2D LINE

RATIOS DIAGNOSTICS Having introduced the interactive ZQE 3D line ratio diagrams as a new tool to study the multi-dimensional galaxy emission line space, we turn our attention to one possible application: the definition of new diagnostic diagrams to separate H II-like and AGN-like objects independently of the standard line ratio diagrams. To that end, we have visually and interactively inspected all twenty-four ZQE diagrams, and selected a subsample of thirteen in which the starburst sequence and the AGN sequence are best separated. The other eleven diagrams (that do no have a ZE diagnostic associated to in Table 3) do not show an evident separation between the AGN and starburst sequences. Hence, these diagrams are less suitable for the kind of analysis presented here. As we discuss in Section 7, these ZQE diagrams may become of interest in a different type of application, for example when looking at the inherent structure of the AGN branch in the multi-dimensional line ratio space of galaxy spectra, which will be explored in a separate article. 5.1. The ZE x1 x2 x3 (φ; θ) diagrams The original MAPPINGS IV simulation grids created by Dopita et al. (2013) define a set of surfaces in the

6

Vogt et al.

TABLE 3 All possible ZQE diagrams combining one line ratio from each Category I, II and III defined in Table 2, and existence of an associated ZE diagnostic. Name

ZE diagnostic ?

Ratio 1

Ratio 2

Ratio 3

log

[N ii] [O ii]

log

[O iii] [O ii]

log

[O iii] [Hβ]

yes

ZQE acg

log

[N ii] [O ii]

log

[O iii] [O ii]

log

[N ii] [Hα]

yes

ZQE ach

log

[N ii] [O ii]

log

[O iii] [O ii]

log

[S ii] [Hα]

no

ZQE aci

log

[N ii] [O ii]

log

[O iii] [O ii]

log

[O i] [Hα]

no

ZQE adf

log

[N ii] [O ii]

log

[O iii] [S ii]

log

[O iii] [Hβ]

no

ZQE adg

log

[N ii] [O ii]

log

[O iii] [S ii]

log

[N ii] [Hα]

yes

ZQE adh

log

[N ii] [O ii]

log

[O iii] [S ii]

log

[S ii] [Hα]

no

ZQE adi

log

[N ii] [O ii]

log

[O iii] [S ii]

log

[O i] [Hα]

no

ZQE aef

log

[N ii] [O ii]

log

[O iii] [N ii]

log

[O iii] [Hβ]

yes

log

[N ii] [O ii]

log

[O iii] [N ii]

log

[N ii] [Hα]

yes

ZQE aeh

log

[N ii] [O ii]

log

[O iii] [N ii]

log

[S ii] [Hα]

no

ZQE aei

log

[N ii] [O ii]

log

[O iii] [N ii]

log

[O i] [Hα]

no

ZQE bcf

log

[N ii] [S ii]

log

[O iii] [O ii]

log

[O iii] [Hβ]

no

ZQE bcg

log

[N ii] [S ii]

log

[O iii] [O ii]

log

[N ii] [Hα]

yes

ZQE bch

log

[N ii] [S ii]

log

[O iii] [O ii]

log

[S ii] [Hα]

yes

ZQE bci

log

[N ii] [S ii]

log

[O iii] [O ii]

log

[O i] [Hα]

no

ZQE bdf

log

[N ii] [S ii]

log

[O iii] [S ii]

log

[O iii] [Hβ]

yes

ZQE bdg

log

[N ii] [S ii]

log

[O iii] [S ii]

log

[N ii] [Hα]

yes

ZQE bdh

log

[N ii] [S ii]

log

[O iii] [S ii]

log

[S ii] [Hα]

yes

ZQE bdi

log

[N ii] [S ii]

log

[O iii] [S ii]

log

[O i] [Hα]

no

ZQE bef

log

[N ii] [S ii]

log

[O iii] [N ii]

log

[O iii] [Hβ]

yes

ZQE beg

log

[N ii] [S ii]

log

[O iii] [N ii]

log

[N ii] [Hα]

yes

ZQE beh

log

[N ii] [S ii]

log

[O iii] [N ii]

log

[S ii] [Hα]

yes

ZQE bei

log

[N ii] [S ii]

log

[O iii] [N ii]

log

[O i] [Hα]

no

ZQE acf

ZQE aeg

ZQE line ratio spaces (see Figure 1). For some of the grids, the intrinsic curvature in the third dimension is small, such that it is possible to find a specific pointof-view from which the grid collapses onto itself, with a thickness .0.3 dex. By identifying these specific viewpoints, we effectively identify new (composite) 2D line ratio diagrams - the ZE x1 x2 x3 (φ; θ) diagrams - which rely on the combination of three different line ratios, and in which H II-like objects are degenerate and constrained to a small region in the diagram. These new 2D line ratio diagrams are uniquely defined by 1. the three line ratios involved, and 2. the angles φ and θ defining the viewing angle in the ZQE space defined by the ratios.

Here φ and θ are defined following the standard spherical coordinates convention (see Figure 2). We adopt the convention that the roll angle ρ = 0 to ensure the uniqueness of each diagram. For reasons highlighted below, we refer to these 2D line ratio diagrams constructed from the projection of a ZQE space as Metallicity-Excitation (ZE) diagrams. With this naming convention, we avoid the confusion which may arise through the use of the standard optical line ratio diagnostic diagrams, or with the more recent Mass-Excitation (MEx) diagram from Juneau et al. (2011, 2014). We introduce the following notation (illustrated in Figure 2), that allows to uniquely identify any ZE diagram (always provided that ρ = 0); ZE x1 x2 x3 (φ; θ)

with

φ ∈ [0, 180[ ; θ ∈ [0, 180[

(6)

where x1 ,x2 and x3 are the three line ratio keys involved (as defined in Table 2). We limit φ to 180 degrees to avoid a mirror version of each diagram. For any given triplet of line ratio values (r1 ; r2 ; r3 ), the ZE x1 x2 x3 (φ; θ) diagram associates a unique doublet of composite line ratios (n1 ; n2 ), defined by : n1 = −r1 sin φ + r2 cos φ n2 = −r1 cos φ cos θ − r2 sin φ cos θ + r3 sin θ

(7) (8)

One should note that because we adopted the convention of ρ = 0, the composite line ratio n1 is simply a combination of the first two ratios r1 and r2 .

Fig. 2.— Schematic illustrating the concept of the ZE x1 x2 x3 (φ; θ) diagram, and the associated notation defined in this article.

5.2. The ZE x1 x2 x3 (φ∗ ; θ∗ ) diagnostics From the twenty-four initial ZQE diagrams listed in Table 3, we have identified thirteen for which: 1. we could find a ZE plane in which the H II regions collapse onto a line with a thickness . 0.3 dex, and for which 2. the starburst branch of the SDSS galaxies is well separated from the AGN-like objects. Hence, we can construct thirteen new composite line ratio diagnostic diagrams to classify galaxies as H II-like

Three-dimensional Line Ratio Diagrams or AGN-like. In the next two subsections, we describe in details how we determine the specific angles φ∗ , θ∗ and the diagnostic line parameters for each of the ZE diagrams. 5.2.1. Identifying φ∗ and θ∗ : manual vs. automated approach

We define (θ∗ ; φ∗ ) the specific values of φ and θ which define the thirteen ZE diagrams suitable to classify galaxies as H II-like or AGN-like. Each ZE x1 x2 x3 (φ∗ , θ∗ ) diagram is shown in Figure 3 , 4 and 5. The corresponding ZE x1 x2 x3 (φ∗ ; θ∗ ) denomination is shown in the top left corner of each diagram. For clarity, the x and y axes are labelled with the complete n1 and n2 composite line ratio equations, derived from Eqs. 7 and 8. All the parameters of the thirteen ZE diagrams are also summarised in Table 4. In each diagram, we show to the top right the median error associated with the SDSS data points, given the mix of line ratios involved. Juneau et al. (2014) observed (in a set of duplicate observations extracted from SDSS DR7) that the error associated with line ratios are comparatively smaller than those associated with individual line fluxes. Hence, our median errors (computed from the individual line errors) reported in the different panels of Figure 3, 4 and 5 can be regarded as upper bounds on the real errors of the composite line ratios. These median errors can be compared to the theoretical displacement that Rαβ =3.1 (instead of 2.86) would imprint on the data. The circle-and-bar traces the intensity and direction (from the circle center outwards) of the total ζ spatial shift (see Eq. 5). The ζ shift is always similar to or smaller than the median measurement errors, and largely influenced by the log[N II]/[O II] ratio. The values of φ∗ and θ∗ have been found by interactive inspection of the ZQE diagrams10 . It should be noted here that in all cases, φ∗ and θ∗ are not tightly constrained. Typically, a variation of ±2 degrees will not significantly modify the general appearance of the projection, so that we restricted our choice to integer values of φ∗ and θ∗ . We find that the theoretical grids created with MAPPINGS IV have a slightly different curvature depending on the chosen value of κ; for most ZE diagrams shown in Figure 3, 4 and 5, a different value of κ could influence the choice of the angles φ∗ and θ∗ by ±2 degrees. The values quoted in Table 4 are our favoured ones for κ = 20. Our choices of φ∗ and θ∗ were guided jointly by the appearance of the theoretical models, individual H II regions, and the SDSS starburst branch. Specifically, we first used the model grids to identify a “first-order” point of view from which the grids collapse onto themselves. We then turned our attention to the cloud of SDSS galaxies, and specifically to the starburst branch, to fine-tune the final choice of φ∗ and θ∗ so that the observational data appears at its thinnest. For all the ZE diagrams but two, the MAPPINGS IV simulation grid (marked by filled circles coloured as a function of the corresponding oxygen abundance of the model) is narrow and degenerate, mostly in the q direction. Hence, the x axis of these ZE diagrams can be associated with a metallicity (Z) di10 The capability to handle 3D models and structures interactively is an intrinsic characteristic of Mayavi2.

7

rection. By contrast, most of the differentiation between starburst-like and AGN-like objects is achieved in the y direction, which can therefore be seen as the excitation or E direction, which is the basis of our chosen nomenclature. For the particular case of the ZE beh and ZE bch diagrams, a two dimensional twist inherent to the simulation grid makes it impossible to find a point-of-view from which the grid collapses for the entire metallicity range. In that case, we chose φ∗ and θ∗ so that the H II space is most degenerate in the area of largest confusion between H II-like and AGN-like objects. Identifying a specific viewpoint on the 3D distribution of SDSS observational data points is somewhat reminiscent of the notion of the Fundamental Plane (FP) for early-type galaxies (Dressler et al. 1987; Djorgovski & Davis 1987). In that situation, the identification of the parameters of the best-fit FP is often performed automatically, for example by computing the direction of smallest scatter in the data (e.g. Jorgensen et al. 1996), or with similar but more sophisticated approaches (e.g. Bernardi et al. 2003; Saulder et al. 2013). While it is in principle not impossible to perform an analytical identification of φ∗ and θ∗ , it is in practice less straightforward than our adopted manual solution. First, the structure of the 3D distribution of SDSS galaxies in the ZQE diagrams is significantly more complex than that of a plane. Second, the dataset contains both H II-like and AGN-like objects, but in the present case one only is interested in collapsing the starburst branch onto itself - not the entire cloud of data points. If it is possible to identify and track the location of the starburst branch “by eye”, it is significantly more complex to do so analytically and without any prior knowledge of the classification of the different objects. As we have found manually, any choice of φ∗ and θ∗ is not tightly constrained, and could vary by ±2 degrees without significantly affecting the structure of the ZE diagram. Under this circumstance and at this point in time, our manual identification of φ∗ and θ∗ appears as satisfactory and useful as any analytical approach. Especially, analytical determinations of φ∗ and θ∗ would still depend on the underlying dataset and the chosen methodology, and would therefore not be “unique” (as is the case for the FP parameters, see Bernardi et al. 2003). The implementation of an automated routine to identify φ∗ and θ∗ is outside the scope of this paper, but ought to be explored in the future as the quality of the observational data points and theoretical datasets improves further. For example, a spaxel-based analysis relying on ongoing or upcoming IFU surveys such as Califa (S´anchez et al. 2012), SAMI (Croom et al. 2012) or MANGA could better differentiate between the core and the outskirts of galaxies, and possibly reduce the inherent confusion at the interface between star-formation dominated and AGN-dominated objects (Maragkoudakis et al. 2014; Davies et al. 2014). Principal Component Analysis (PCA) is a statistical technique which can identify directions of interest in multi-dimensional datasets by calculating the successive normal directions of maximum variance (see e.g. Francis & Wills 1999, for a brief introduction). When performing a PCA analysis, the main challenge resides in interpreting these directions of interest, and connecting them to the physical world. The approach we adopt for

8

Vogt et al.

II] [O III] [N II] n2 = -0.018 log[N [O II] + 0.207 log [S II] + 0.978 log H

creating the ZE diagrams (and associated diagnostics) follows the opposite path. Here, we use direct physical insight to separate line ratios into three complementary categories, and only then, once we have constructed the corresponding ZQE space, inspect it interactively to find point-of-views of interest. The interactive aspect of our approach is especially useful in allowing us to compare at the same time the grids of theoretical models, the individual measurements of H II regions, and SDSS galaxies. Of course, the prime advantage of PCA is that it is not restricted to three-dimensional spaces. That is, a PCA analysis could be applied to the entire multi-dimensional line ratio space of galaxies, unlike the ZQE diagrams approach, which for obvious reasons cannot probe beyond three dimensions. Hence, while a detailed comparison is outside the scope of this article, the PCA approach and the ZQE approach are (conceptually) very complimentary. In any situation, to avoid misunderstandings and ensure repeatability, we strongly advise any use of the ZE diagrams to clearly state the values of φ and θ employed, along with the line ratios involved, which are required to uniquely define any ZE diagram (see Section 5.1 and Eq. 6).

12+log(O/H) 7.50 7.75 8.00 8.25 8.50 8.75 9.00 9.25 0.5

ZEadg (95°;102°)

0.0 0.5 1.0 1.5 0.5

0.0

n1 = -0.996

0.5 II] log[N [O II]

- 0.087

1.0

1.5

] log[O[S III II]

Fig. 3.— The ZE adg (95◦ ;102◦ ) diagram. The diagram name and associated values of (φ∗ , θ∗ ) are shown in the top-left corner for completeness. H II-like and AGN-like SDSS galaxies are in grey. Uncertain galaxies (based on all ZE diagnostics) are represented by density contours (5%, 20%, 40% and 80% of the maximum density). The round coloured dots (connected by the dotted lines) correspond to the MAPPINGS IV models from Dopita et al. (2013). These provide guidance about the theoretical shape of the H ii regions space. The van Zee et al. (1998) points are represented by small squares with 75% opacity, and the measurements from NGC 5427 are marked with small triangles. All measured H II regions are color-coded according to their oxygen abundance. The black thick line traces our diagnostic line separating the H ii-like objects from the AGN-like ones, for which we adopt a 3rd degree polynomial functional form. The black cross (top right) indicates the median error associated with the given combination of SDSS flux ratios, and the circle-and-bar symbol marks the intensity and direction (taken from the circle center outwards) of the displacement associated with Rαβ =3.1 instead of 2.86.

5.2.2. Defining the diagnostic lines For each ZE x1 x2 x3 (φ∗ ; θ∗ ) diagram illustrated in Figure 3, 4 and 5, we define a 3rd order polynomial that separates the H II-like objects (below the line) and the AGN-like objects (above the line). The semi-empirical polynomial coefficients α, β, γ and δ are summarised in Table 5, where the line equation is defined by y = f (n1 ) = α(n1 )3 + β(n1 )2 + γ(n1 ) + δ.

(9)

This approach is similar to that used by Kewley et al. (2001a) and Kauffmann et al. (2003b) to define diagnostic lines for the classical optical line ratio diagnostic diagrams, although the chosen functional forms are different. The theoretical grids do not match the envelope of the observations of H II regions perfectly (see Figures 3, 4 and 5). This is especially true for ZE diagrams involving the [S II] lines, which as noted by Dopita et al. (2013) appear to be 0.1 dex too weak in the models. There exist several possible origins for the theoretical mismatch. At the low abundance end in particular, some H II regions may possibly have a higher electron density than expected (up to ne w 100 cm3 ) (Nicholls et al., in preparation). At the high-abundance end, all lines become very sensitive to the electron temperature, which varies very rapidly through the models. Thus, small changes in the geometry of the ionised gas (assumed to be spherically symmetric in the models) can make large differences in the predicted emission line spectrum. The underlying stellar synthesis models may also be largely responsible for the offset between the theoretical grids and the SDSS galaxies (especially for line ratios involving the [S II] lines) if these theoretical models do not produce enough far-UV ionizing photons, as suggested by Kewley et al. (2001a) and Levesque et al. (2010). Lastly, we note that the spacing between the two highest abundance set of simulations are ∼2-3 times larger than the spacing between the other abundance sets. As a result, linearly interpolating (as traced by the dotted lines in Figures 3, 4 and 5) can be a poorer estimation and result in a larger mismatch between the theoretical grid and the observations. Given the mismatch between the shape of the model grids and the observational data points in some of the ZE diagrams, we use the theoretical models as a general guide, but choose the final coefficients α, β, γ and δ so that the diagnostic lines trace the full extent of the starburst sequence of the SDSS galaxies in all cases. Hence, keeping in mind that we indirectly rely on the theoretical models in the manual determination procedure for the values of φ∗ and θ∗ (see Section 5.2.1), the different ZE diagnostics do not depend explicitly on the MAPPINGS IV grids. In practice, the diagnostic line coefficients are identified as follows. We first choose manually a series of fiveto-seven positions in the ZE diagram, spaced by 0.2-0.5 dex along the x-direction, defining a first-order separation between H II-like and AGN-like objects. We subsequently obtain the corresponding polynomial coefficients by performing a least-square minimisation of a 3rd order polynomial to these data-points using the Python im-

ZEacf (96°;50°)

0.6 0.4 0.2 0.0 0.2 0.4 0.5

0.0

0.5

1.0

1.5

0.5

ZEacg (96°;104°)

0.0 0.5 1.0 1.5 0.5

0.0

0.5

1.0

1.5

12+log(O/H) 7.50 7.75 8.00 8.25 8.50 8.75 9.00 9.25

12+log(O/H) 7.50 7.75 8.00 8.25 8.50 8.75 9.00 9.25

0.5 0.0 0.5 1.0 0.5

0.0

0.5

1.0

1.5

0.5

ZEaeg (95°;104°)

0.0 0.5 1.0 1.5 0.5

0.0

0.5

1.0

1.5

II] [O III] n1 = -0.996 log[N [O II] - 0.087 log [N II]

II] [O III] n1 = -0.996 log[N [O II] - 0.087 log [N II]

12+log(O/H) 7.50 7.75 8.00 8.25 8.50 8.75 9.00 9.25

12+log(O/H) 7.50 7.75 8.00 8.25 8.50 8.75 9.00 9.25

ZEbcg (75°;105°)

0.0 0.5 1.0 1.5 2.0

12+log(O/H) 7.50 7.75 8.00 8.25 8.50 8.75 9.00 9.25

II] [O III] n1 = -0.995 log[N [O II] - 0.105 log [O II]

ZEaef (95°;53°)

0.5

9

[N II] ] n1 = -0.995 log[O - 0.105 log[O[OIII II] II]

II] [O III] [N II] n2 = -0.021 log[N [O II] + 0.241 log [N II] + 0.97 log H

0.8

[N II] ] n2 = -0.025 log[O + 0.241 log[O[OIII + 0.97 log[NHII] II] II]

12+log(O/H) 7.50 7.75 8.00 8.25 8.50 8.75 9.00 9.25

1.0

0.5

0.0

0.5

1.0

] n2 = 0.11 log[N[S IIII]] + 0.441 log[O[OIII + 0.891 log[SHII] II]

] n2 = 0.067 log[N[S IIII]] + 0.25 log[O[OIII + 0.966 log[NHII] II]

II] [O III] [O III] n2 = 0.052 log[N [O II] - 0.6 log [N II] + 0.799 log H

[N II] ] n2 = 0.067 log[O - 0.639 log[O[OIII + 0.766 log[OHIII] II] II]

Three-dimensional Line Ratio Diagrams

] n1 = -0.966 log[N[S IIII]] + 0.259 log[O[OIII II]

ZEbch (76°;117°)

0.0 0.5 1.0 1.0

0.5

0.0

0.5

1.0

] n1 = -0.97 log[N[S IIII]] + 0.242 log[O[OIII II]

Fig. 4.— Same as Figure 3, for the other ZE diagnostics involving [O ii].

plementation of the IDL11 non-linear least-square minimization routine mpfit (Markwardt 2009). Since we set these diagnostic lines manually and independently 11

Interactive Data Language

for each diagram, using the theoretical grid for guidance only, and given that each diagnostic is subject to both observational errors and theoretical uncertainties, it is possible that an SDSS galaxy classified as H II-like by one diagnostic will be classified as AGN-like by others.

ZEbdf (80°;58°)

0.4 0.2 0.0 0.2 0.4 0.6 0.5

0.2

0.0

0.5

1.0

0.5

ZEbdg (80°;101°)

0.0 0.5 1.0 1.5 0.5

0.0

0.5

1.0

] n1 = -0.985 log[N[S IIII]] + 0.174 log[O[S III II]

12+log(O/H) 7.50 7.75 8.00 8.25 8.50 8.75 9.00 9.25

12+log(O/H) 7.50 7.75 8.00 8.25 8.50 8.75 9.00 9.25

ZEbdh (81°;110°)

0.0 0.2 0.4 0.6 0.8 1.0 0.5

0.5

12+log(O/H) 7.50 7.75 8.00 8.25 8.50 8.75 9.00 9.25

] n1 = -0.985 log[N[S IIII]] + 0.174 log[O[S III II]

0.0

0.5

1.0

] n2 = -0.125 log[N[S IIII]] - 0.589 log[O[NIII + 0.799 log[OHIII] II]

0.6

ZEbef (78°;53°)

0.5

0.0

0.5 1.0

0.5

0.0

0.5

1.0

] n1 = -0.988 log[N[S IIII]] + 0.156 log[O[S III II]

] n1 = -0.978 log[N[S IIII]] + 0.208 log[O[NIII II]

12+log(O/H) 7.50 7.75 8.00 8.25 8.50 8.75 9.00 9.25

12+log(O/H) 7.50 7.75 8.00 8.25 8.50 8.75 9.00 9.25

ZEbeg (79°;103°)

0.0 0.5 1.0 1.5 1.0

0.5

0.0

0.5

1.0

] n2 = 0.095 log[N[S IIII]] + 0.412 log[O[NIII + 0.906 log[SHII] II]

] n2 = 0.054 log[N[S IIII]] + 0.338 log[O[S III + 0.94 log[SHII] II] ] n2 = 0.043 log[N[S IIII]] + 0.221 log[O[NIII + 0.974 log[NHII] II]

12+log(O/H) 7.50 7.75 8.00 8.25 8.50 8.75 9.00 9.25

] n2 = 0.033 log[N[S IIII]] + 0.188 log[O[S III + 0.982 log[NHII] II]

Vogt et al.

] n2 = -0.092 log[N[S IIII]] - 0.522 log[O[S III + 0.848 log[OHIII] II]

10

] n1 = -0.982 log[N[S IIII]] + 0.191 log[O[NIII II]

0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

ZEbeh (77°;115°)

1.0

0.5

0.0

0.5

1.0

] n1 = -0.974 log[N[S IIII]] + 0.225 log[O[NIII II]

Fig. 5.— Same as Figure 3, but for the ZE diagnostics not involving [O ii].

However, because we now have thirteen diagnostics, we can combine them to ensure consistency and reduce the classification uncertainty. To that end, we separate all SDSS galaxies into three groups:

• H II-like: galaxies classified as H II-like by all thirteen ZE diagnostics, • AGN-like: galaxies classified as AGN-like by all thirteen ZE diagnostics, and

Three-dimensional Line Ratio Diagrams

11

TABLE 4 ZE diagrams, and their associated parameters. Name

φ∗

θ∗

n1

n2

ZE acf

96

50

−0.995 · log

[N ii] [O ii]

− 0.105 · log

[O iii] [O ii]

ZE acg

96

104

−0.995 · log

[N ii] [O ii]

− 0.105 · log

[O iii] [O ii]

−0.025 · log

[N ii] [O ii]

+ 0.241 · log

[O iii] [O ii]

+ 0.970 · log

[N ii] [Hα]

ZE adg

95

102

−0.996 · log

[N ii] [O ii]

− 0.087 · log

[O iii] [O ii]

−0.018 · log

[N ii] [O ii]

+ 0.207 · log

[O iii] [O ii]

+ 0.978 · log

[N ii] [Hα]

ZE aef

95

53

−0.996 · log

[N ii] [O ii]

− 0.087 · log

[O iii] [N ii]

+0.052 · log

[N ii] [O ii]

− 0.600 · log

[O iii] [N ii]

+ 0.799 · log

[O iii] [Hβ]

ZE aeg

95

104

−0.996 · log

[N ii] [O ii]

− 0.087 · log

[O iii] [N ii]

−0.021 · log

[N ii] [O ii]

+ 0.241 · log

[O iii] [N ii]

+ 0.970 · log

[N ii] [Hα]

ZE bcg

75

105

−0.966 · log

[N ii] [S ii]

+ 0.259 · log

[O iii] [O ii]

+0.067 · log

[N ii] [S ii]

+ 0.250 · log

[O iii] [O ii]

+ 0.966 · log

[N ii] [Hα]

ZE bch

76

117

−0.970 · log

[N ii] [S ii]

+ 0.242 · log

[O iii] [O ii]

+0.110 · log

[N ii] [S ii]

+ 0.441 · log

[O iii] [O ii]

+ 0.891 · log

[N ii] [Hα]

ZE bdf

80

58

−0.985 · log

[N ii] [S ii]

+ 0.174 · log

[O iii] [S ii]

−0.092 · log

[N ii] [S ii]

− 0.522 · log

[O iii] [S ii]

+ 0.848 · log

[O iii] [Hβ]

ZE bdg

80

101

−0.985 · log

[N ii] [S ii]

+ 0.174 · log

[O iii] [S ii]

+0.033 · log

[N ii] [S ii]

+ 0.188 · log

[O iii] [S ii]

+ 0.982 · log

[N ii] [Hα]

ZE bdh

81

110

−0.988 · log

[N ii] [S ii]

+ 0.156 · log

[O iii] [S ii]

+0.054 · log

[N ii] [S ii]

+ 0.338 · log

[O iii] [S ii]

+ 0.940 · log

[S ii] [Hα]

ZE bef

78

53

−0.978 · log

[N ii] [S ii]

+ 0.208 · log

[O iii] [N ii]

−0.125 · log

[N ii] [S ii]

− 0.589 · log

[O iii] [N ii]

+ 0.799 · log

[O iii] [Hβ]

ZE beg

79

103

−0.982 · log

[N ii] [S ii]

+ 0.191 · log

[O iii] [N ii]

+0.043 · log

[N ii] [S ii]

+ 0.221 · log

[O iii] [N ii]

+ 0.974 · log

[N ii] [Hα]

ZE beh

77

115

−0.974 · log

[N ii] [S ii]

+ 0.225 · log

[O iii] [N ii]

+0.095 · log

[N ii] [S ii]

+ 0.412 · log

[O iii] [N ii]

+ 0.906 · log

[S ii] [Hα]

• uncertain: galaxies for which the thirteen ZE diagnostics are inconsistent. In Figure 3, 4 and 5, density contours delineate the location of SDSS galaxies having an uncertain classification. The contours have been obtained by distributing all the galaxies with uncertain classification in a regular grid with resolution of 0.03 dex, with the subsequent smoothing of the grid with a symmetric gaussian filter of 0.15 dex in radius (5 grid elements). As can be expected, the uncertain galaxies are clustered around each of the diagnostic lines, with the 20% contour within ±0.1 dex of the diagnostic line. Using a manual and iterative approach, we have adapted the parameters of each of the diagnostic equations to minimise the number of uncertain galaxies. Following this approach, we reduced the number of galaxies with uncertain classification to 2636 (2.5% of a total of 105070 objects). We have 88918 H II-like galaxies (84.6%) and 13516 galaxies classified as AGN-like (12.9%), as classified by the ZE diagnostics. Improving the overall agreement between the different diagnostics required in some cases to alter the shape of the diagnostic lines, especially for high metallicities. Because the SDSS points are not distributed uniformly, very small modifications of the diagnostic line in denser regions can strongly influence the overall agreement of the different diagnostics. Since we rely on 3rd order polynomials, the inner-most regions of the diagnostic lines are very much influenced by the slope at higher (and lower) metallicities. In other words, the lack of observations make it impossible to tightly constrain the position of the diagnostic line in the outer-most region of the different ZQE diagrams. We examine the consistency of each of these ZE diagnostics in more detail in the next subsection. This is not to be confused with the validity of the final classification itself, which we examine in Section 6.1. In the

+0.067 · log

[N ii] [O ii]

− 0.639 · log

[O iii] [O ii]

+ 0.766 · log

[O iii] [Hβ]

TABLE 5 Starburst diagnostic line parameters for each ZE diagram. Name

α

β

γ

δ

ZE acf

−0.059

−0.024

+0.676

−0.005

ZE acg

+0.005

−0.124

+0.020

−0.445

ZE adg

−0.034

−0.071

+0.091

−0.382

ZE aef

−0.013

−0.082

+0.133

−0.008

ZE aeg

−0.032

−0.079

+0.268

−0.459

ZE bcg

−0.101

−0.311

−0.216

−0.481

ZE bch

−0.132

−0.280

+0.700

−0.437

ZE bdf

−0.283

−0.368

+0.851

+0.066

ZE bdg

−0.118

−0.307

−0.171

−0.382

ZE bdh

−0.238

−0.374

+0.774

−0.366

ZE bef

−0.013

−0.157

+0.186

+0.055

ZE beg

−0.097

−0.222

+0.034

−0.380

ZE beh

−0.221

−0.289

+0.920

−0.350

Appendix, we show for completeness the ZE diagrams that best collapse the grid of photoionization models in the eleven ZQE spaces for which we did not derive any ZE diagnostic. These diagrams were not selected as reliable diagnostics because of the high confusion between the starburst and AGN branch of the SDSS galaxies. In Figures 13 and 14, the confusion is emphasized by showing the density contours of galaxies with uncertain classification. Although the final ZE classification and hence the density contours of uncertain galaxies were de-

Vogt et al.

rived “after” the visual selection of ZQE diagrams with a clean separation between the starburst and AGN branch of SDSS galaxies, these contours act as an a posteriori confirmation of the initial selection. In every ZE diagram shown in Figure 13 and 14 the uncertain galaxies spread out over large areas (>0.2 dex), unlike in the ZE diagnostic diagrams listed in Table 4. 5.3. Consistency of the ZE diagnostics The thirteen ZE diagnostics defined in Table 5 all rely on a subset of nine line ratios, so that they are not strictly independent from one another. To better understand this connection, we focus our attention on the 2636 (2.5%) galaxies with an uncertain classification. We introduce the quantity η(ZE x1 x2 x3 ) as the percentage of uncertain galaxies classified as AGN-like by a particular ZE x1 x2 x3 diagnostic. The value of η for the thirteen ZE diagnostics is shown in Figure 6. A low value of η indicates a diagnostic which is too lax and will classify most uncertain galaxies as H ii-like. On the other hand, a high value of η indicates a diagnostic which is too tight. In such a case, the majority of the uncertain galaxies are classified as being AGN-like by the diagnostic concerned. All thirteen ZE diagnostics have 40%< η(ZE x1 x2 x3 )